Dynamic gradient models for the sub-grid scale stress tensor and scalar flux vector in large eddy simulation

A number of dynamic variants of the modulated gradient model (MGM) for the sub-grid scale (SGS) stress tensor and the SGS scalar flux vector are developed and evaluated a posteriori in large eddy simulations of neutral and stably stratified turbulent channel flow. Two dynamic procedures are evaluated: one based on the local equilibrium hypothesis (called local-dynamic models) and one based on the global equilibrium and steady state hypotheses (global-dynamic models). These local-dynamic (LD) and global-dynamic (GD) versions of MGM are found to be much more accurate than the constant coefficient MGM in neutral turbulent channel flow at friction Reynolds numbers of 180 and 590. The constant coefficient MGM and GD-MGM are also found to yield the correct asymptotic behaviour close to the wall, which indicates the suitability of coupling the MGM kernel with the GD procedure. For the SGS scalar flux vector, LD and GD versions of the MGM are evaluated along with LD and GD versions of the recently proposed Smagorinsky-gradient (SGM) and Vreman-gradient (VGM) models. Tests in neutral and stably stratified channel flow at friction Reynolds number of 180 and friction Richardson numbers of 0 and 18 reveal that all six dynamic SGS scalar flux vector models are able to reproduce first-order and second-order turbulent statistics accurately. The simulations help further establish the stability and accuracy of SGM and VGM, which have not been tested previously. None of the dynamic gradient-based SGS scalar flux vector models are found to yield the correct asymptotic behaviour, however, and this issue needs further investigation.     

Large eddy simulation of channel flow with and without periodic constrictions using the explicit algebraic subgrid-scale model

We analyse the performance of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) in large eddy simulation (LES) of plane channel flow and the flow in a channel with streamwise periodic hill-shaped constrictions (periodic hill flow) which induce separation. The LESs are performed with the Code_Saturne which is an unstructured collocated finite volume solver with a second-order spatial discretisation suitable for LES of incompressible flow in complex geometries. At first, performance of the EASSM in LES of plane channel flow at two different resolutions using the Code_Saturne and a pseudo-spectral method is analysed. It is observed that the EASSM predictions of the mean velocity and Reynolds stresses are more accurate than the conventional dynamic Smagorinsky model (DSM). The results with the pseudo-spectral method were, in general, more accurate. In the second step, LES with the EASSM of flow separation in the periodic hill flow is compared to LES with the DSM, no SGS model and a highly resolved LES data using the DSM. Results show that the mean velocity profiles, the friction and pressure coefficients, the length and shape of the recirculation bubble, as well as the Reynolds stresses are considerably better predicted by the EASSM than the DSM and the no SGS model simulations. It was also observed that in some parts of the domain, the resolved strain-rate and SGS shear stress have the same sign. The DSM cannot produce a correct SGS stress in this case, in contrast to the EASSM.     

不同亚格子模型在亚声速槽道流大涡模拟中的应用对比

湍流边界层流动是一种广泛存在于飞行器内部和外部的流动现象，是基础理论和模型验证的重要研究对象.能够捕捉大部分流动细节且计算量适中的大涡模拟（large-eddy simulation，LES）方法在湍流数值模拟中得到了越来越广泛的应用.文章基于格心有限差分方法，使用4阶紧致中心格式离散N-S方程无黏项，分别应用5种不同的亚格子（subgrid-scale，SGS）模型，即隐式，SM（Smagorinsky model），DSM（dynamic Smagorinsky model），WALE（wall-adapting local eddy-viscosity model）和CSM（coherent structures model），对Re = 3 000，Ma = 0.5的等温壁面槽道流动进行了大涡模拟研究.与实验值和直接数值模拟（direct numerical simulation，DNS）结果对比后发现，流场平均温度、平均密度等热力学量以及平均流向速度对亚格子模型不敏感，不适宜作为判断模型优劣的判据.亚格子模型在壁面附近的耗散越大，壁面摩擦速度以及阻力系数就越小.对于与速度相关的脉动量来说，不同模型得到的结果在壁面和脉动峰值附近误差比较大，中心线附近较小；显式模型结果在流向速度峰值处均高于参考值，而在展向和壁面法向速度脉动峰值处则均偏低.考虑显式的4种模型在壁面附近的涡黏系数分布，DSM和CSM曲线满足涡黏系数与无量纲壁面距离3次方成正比的分布规律，SM曲线斜率偏小而WALE曲线斜率偏大.      

An improved dynamic subgrid-scale model and its application to large eddy simulation of rotating channel flows

Rotating turbulence occurs extensively in nature and engineering circumstances. Meanwhile, understanding physical mechanisms of the rotating turbulence is important to the fundamental research of turbulence. The turbulent flow in rotating frames undergoes two kinds of Coriolis force effects. First, a secondary flow is induced in the case that there is a mean vorticity component perpendicular to the rotating axis. Second, there are augmenting or suppressing effects on the turbulence if there i…     

A new mixed subgrid-scale model for large eddy simulation of turbulent drag-reducing flows of viscoelastic fluids

A mixed subgrid-scale(SGS) model based on coherent structures and temporal approximate deconvolution(MCT) is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation(LES) of turbulent dragreducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence(FHIT) with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation(DNS) results. Compared with the LES results using the temporal approximate deconvolution model(TADM) for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number.For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.     

A priori evaluation of large eddy simulation subgrid-scale scalar flux models in isotropic passive-scalar and anisotropic buoyancy-driven homogeneous turbulence

Direct numerical simulation (DNS) of passive (non-buoyant) and active (buoyant) scalar homogeneous turbulence is carried out using a standard pseudo-spectral numerical method. The flow settings simulated include stationary forced and decaying passive-scalar turbulence, as well as decaying anisotropic active-scalar turbulence. The Schmidt number is unity in all cases. The results are compared with, and are found to be in very good agreement with, previous similar DNS studies. The well-validated DNS data are divided into 19 sets, and are employed to study different large eddy simulation (LES) subgrid-scale (SGS) models for the SGS scalar flux. The models examined include three eddy-viscosity-type models (Smagorinsky, Vreman and Sigma with a constant SGS Schmidt number), a Dynamic Structure model and two versions of the Gradient (Gradient and Modulated Gradient) model. The models are investigated with respect to their ability to predict the orientation, and the magnitude, of the SGS scalar flux. Eddy-viscosity models are found to predict the magnitude of the SGS scalar flux accurately, but are poor at predicting the orientation of the SGS scalar flux. The Dynamic Structure and Gradient models are better than eddy-viscosity models at predicting both the magnitude and direction. However, neither of them can be realised in an actual LES, without carrying additional transport equations. Based on these observations, four new models are proposed – combining directions from Dynamic Structure and Gradient models, and magnitudes from Smagorinsky and Vreman eddy-viscosity models. These models are expected to be better than eddy-viscosity and Modulated Gradient models, and this is confirmed by preliminary a posteriori tests.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

On the effect of an anisotropy-resolving subgrid-scale model on large eddy simulation predictions of turbulent open channel flow with wall roughness

A large eddy simulation (LES) was conducted of turbulent flow in a channel with a rough wall on one side and a free surface on the other by adopting an anisotropy-resolving subgrid-scale (SGS) model. A shear Reynolds number of Re_τ = 395 was used based on the mean friction velocity and channel height. To investigate the grid dependency of the LES results caused by the SGS model, three grid resolutions were tested under the same definition of a roughness shape by using the immersed boundary method. The results obtained were compared with direct numerical simulation data with and without the wall roughness and those without the extra anisotropic term. The primary focus was on how the present anisotropic SGS model with coarser grid resolutions can properly provide the effects of roughness on the mean velocity and turbulent stresses, leading to a considerable reduction of the computational cost of LES.     

二维槽道湍流拟序结构的大涡模拟

本文采用大涡模拟的方法,对二维槽道湍流流动进行了数值模拟。采用Chorin的分步投影法求解大尺度涡运动的Navier-Stokes方程,小尺度涡采用三种亚格子（SGS）模式分别模拟,给出了不同亚格子涡粘性模式下的模拟结果。对固壁面采用了壁函数。模拟结果再现了二维槽道流动拟序结构的发展演变过程。通过对不同入口速度下的瞬态流场的比较,揭示了入口速度分布对流场的影响。     

Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method

In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or test-filtering of super-grid turbulence dynamics and subsequent use of scale-invariance for two levels, circumvents the need for empiricism in determining the magnitude of the model coefficient of the SGS models. We employ the multiple relaxation times (MRT) formulation of LBM with a forcing term, which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non-hydrodynamic modes, for simulation of the grid-filtered dynamics of large-eddies. The dynamic procedure is illustrated for use with the common Smagorinsky eddy-viscosity SGS model, and incorporated in the LBM kinetic approach through effective relaxation time scales. The strain rate tensor in the SGS model is locally computed by means of non-equilibrium moments of the MRT-LBM. We also discuss proper sampling techniques or test-filters that facilitate implementation of dynamic models in the LBM. For accommodating variable resolutions, we employ conservative, locally refined grids in this framework. As examples, we consider the canonical anisotropic and inhomogeneous turbulent flow problem, i.e. fully-developed turbulent channel flow at two different shear Reynolds numbers Re_∗ of 180 and 395. The approach is able to automatically and self-consistently compute the values of the Smagorinsky coefficient, C_S. In particular, the computed value in the outer or bulk flow region, where turbulence is generally more isotropic, is about 0.155 (or the model coefficient ) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and approaches towards zero near walls, reflecting the dampening of turbulent length scales near walls. The computed turbulence statistics at these Reynolds numbers are also in good agreement with prior data. The paper also discusses a procedure for incorporation of more general scale-similarity based SGS stress models.     

SUPERCONDUCTING MICROSTRIP LINE MODEL STUDIES AT MILLIMETRE AND SUB-MILLIMETRE WAVES

This paper presents results of superconducting microstrip transmission line simulation for the frequency range 100–1100 GHz. The simulation is used to calculate the characteristic impedance and the wave propagation constant in a superconducting microstrip line having different geometry. Indeed, modelling provides the only tool for designing superconducting microstrip-based circuits at millimetre and sub-millimetre wavelengths because no direct measurements of such a line can be made at this wavelengths and at cryogenic temperature of 4 K with ultimate accuracy. Niobium, as the most commonly exploited superconducting material, was used for the modelling, though the same approach would work for any different BCS superconductor. In order to evaluate the model accuracy, we have made an extensive comparison study of the superconducting microstrip models known from earlier publications, performed numerical simulations using 3D EM — solver, HFSS, and used a new model introduced in this paper with all simulation result plotted in the paper.     

A velocity-estimation subgrid model constrained by subgrid scale dissipation

Purely dissipative eddy-viscosity subgrid models have proven very successful in large-eddy simulations (LES) at moderate resolution. Simulations at coarse resolutions where the underlying assumption of small-scale universality is not valid, warrant more advanced models. However, non-eddy viscosity models are often unstable due to the lack of sufficient dissipation. This paper proposes a simple modeling approach which incorporates the dissipative nature of existing eddy viscosity models into more physically appealing non-eddy viscosity SGS models. The key idea is to impose the SGS dissipation of the eddy viscosity model as a constraint on the non-eddy viscosity model when determining the coefficients in the non-eddy viscosity model. We propose a new subgrid scale model (RSEM), which is based on estimation of the unresolved velocity field. RSEM is developed in physical space and does not require the use of finer grids to estimate the subgrid velocity field. The model coefficient is determined such that total SGS dissipation matches that from a target SGS model in the mean or least-squares sense. The dynamic Smagorinsky model is used to provide the target dissipation. Results are shown for LES of decaying isotropic turbulence and turbulent channel flow. For isotropic turbulence, RSEM displays some level of backward dissipation, while yielding as good results as the dynamic Smagorinsky model. For channel flow, the results from RSEM are better than those from the dynamic Smagorinsky model for both statistics and instantaneous flow structures.     

Direct evaluation of the subgrid scale scalar flux in turbulent premixed flames with conditioned dual-plane stereo PIV

With the dual-plane stereo PIV technique the instantaneous three-dimensional resolved rate-of-strain tensor is directly measured in turbulent premixed flames. Simultaneously, also the instantaneous subgrid scale (SGS) scalar flux is measured with fine resolution, where for the latter term the conditioned particle image velocimetry (CPIV) technique is applied. The subgrid resolution reaches 118 μm, allowing a 9 × 9 resolution of a subgrid filter with width Δ = 1 mm. This combined measurement approach allows the a-priori comparison of models for the SGS scalar flux term with direct measurements which is important for large eddy simulation methods in turbulent premixed flames. Two different flame conditions of a premixed V-shaped turbulent flame are investigated where the turbulence intensity is varied by a factor of nearly three. The instantaneous radial and axial SGS fluxes are compared with the following three models: gradient model with Smagorinsky approach for the turbulent viscosity, Clark model, and extended gradient model with an anisotropy term. None of these models shows a good correlation with the directly measured flux. The anisotropy term alone (being nearly similar to the Clark model) shows, however, a right trend behaviour. An analysis of the data indicates a significant dependency of the experimentally determined SGS flux on the Favre averaged reaction progress (spatially averaged over the SGS area). A relatively simple closure for the SGS flux, which describes the dilatation due to the gasdynamic expansion, and which is a function proportional to , shows a rather good correlation with direct measurement for some of the components. A successful SGS scalar flux model for premixed turbulent flames most likely needs to include at least two different effects.     

Grid and subgrid-scale interactions in viscoelastic turbulent flow and implications for modelling

Using direct numerical simulations of turbulent plane channel flow of homogeneous polymer solutions, described by the Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model, a-priori analyses of the filtered momentum and FENE-P constitutive equations are performed. The influence of the polymer additives on the subgrid-scale (SGS) energy is evaluated by comparing the Newtonian and the viscoelastic flows, and a severe suppression of SGS stresses and energy is observed in the viscoelastic flow. All the terms of the transport equation of the SGS kinetic energy for FENE-P fluids are analysed, and an approximated version of this equation for use in future large eddy simulation closures is suggested. The terms responsible for kinetic energy transfer between grid-scale (GS) and SGS energy (split into forward/backward energy transfer) are evaluated in the presence of polymers. It is observed that the probability and intensity of forward scatter events tend to decrease in the presence of polymers.     

High-order incompressible large-eddy simulation of fully inhomogeneous turbulent flows

The subgrid-scale (SGS) eddy-viscosity model developed by Vreman [Phys. Fluids 16 (2004) 3670] and its dynamic version [Phys. Fluids 19 (2007) 065110] are tested in large-eddy simulations (LES) of the turbulent flow in an Re = 12,000 lid-driven cubical cavity by comparison to the direct numerical simulation (DNS) data of Leriche and Gavrilakis [Phys. Fluids 12 (2000) 1363]. This appears to be the first test of this class of model to flows without any homogeneous flow directions, which is typical of flows in complex geometries. Additional LES predictions at Re = 18,000 and Re = 22,000 are compared to the DNS data of Leriche [J. Sci. Comp. 27 (2006)]. The new LES framework yielded excellent agreement for both the mean velocity and Reynolds stress profiles and matches DNS data better than the more traditional Smagorinsky-based SGS models.     

Assessment of subgrid-scale stress statistics in non-premixed turbulent wall-jet flames

We investigate the heat-release effects on the characteristics of the subgrid-scale (SGS) stress tensor and SGS dissipation of kinetic energy and enstrophy. Direct numerical simulation data of a non-premixed reacting turbulent wall-jet flow with and without substantial heat release is employed for the analysis. This study comprises, among others, an analysis of the eigenvalues of the resolved strain rate and SGS stress tensors, to identify the heat-release effects on their topology. An assessment of the alignment between the eigenvectors corresponding to the largest eigenvalues of these two tensors is also given to provide further information for modelling of the SGS stress tensor. To find out the heat-release effects on the dynamics of the turbulent kinetic energy and enstrophy dissipation, probability density functions (PDFs) and mean values are analysed. The mean SGS shear stress and turbulent kinetic energy both slightly increase in the buffer layer and substantially decrease further away from the wall, due to the heat-release effects. Contrary to the kinetic energy, heat release decreases the mean SGS dissipation of enstrophy in the near-wall region. Moreover, differences in the shapes of the PDFs between the isothermal and exothermic cases indicate changes in the intermittency level of both SGS dissipations. Heat release also increases the SGS stress anisotropy in the near-wall region. Although, the structure of the mean resolved strain-rate tensor only marginally differs between the isothermal and exothermic cases in the near-wall region, substantial differences are observed in the jet area, where compressibility effects are important and heat-release effects are found to promote compression states. The differences in the relative alignment between the SGS stress and resolved strain-rate tensors in the isothermal and exothermic cases are discussed in connection with the differences in the SGS dissipation of kinetic energy.     

Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re_λ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.     

Coupled fluid–structure solver: The case of shock wave impact on monolithic and composite material plates

An unstructured adaptive mesh flow solver, a finite element structure solver and a moving mesh algorithm were implemented in the numerical simulation of the interaction between a shock wave and a structure. In the past, this interaction is mostly considered as one-way in the sense that the shock causes a transient load on the structure while it is reflected uneffected by the impact. A fully coupled approach was implemented in the present work which can account for the effects associated with a mutual interaction. This approach included a compressible flow Eulerian solver of second order accuracy in finite volume formulation for the fluid and a Langargian solver in finite element formulation for the solid structure. A novel implementation of advancing front moving mesh algorithm was made possible with the introduction of a flexible and efficient quad-edge data structure. Adaptive mesh refinement was introduced into the flow solver for improved accuracy as well. Numerical results are further validated by theoretical analysis, experimental data and results from other numerical simulations. Grid dependency study was performed and results showed that the physical phenomena and quantities were independent of the numerical grid chosen in the simulations. The results illuminated complicated flow phenomena and structure vibration patterns, which in order to be detected experimentally require capabilities beyond those of the current experimental techniques. The numerical simulations also successfully modelled the aero-acoustic damping effects on the structure, which do not exist in previous numerical models. Further analysis of the results showed that the mutual interaction is not linear and that the non-linearity arises because the wave propagation in the fluid is not linear and it cascades a non-linear and non-uniform loading on the plate. Non-linearity intensifies when the plate is vibrating at high frequency while the wave propagation speed is low.     

A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

An appraisal is made of several subgrid scale (SGS) viscous/scalar dissipation closures via a priori analysis of direct numerical simulation data in a temporally evolving compressible mixing layer. The effects of the filter width, the compressibility level and the Schmidt number are studied for several models. Based on the scaling of SGS kinetic energy, a new formulation for SGS viscous dissipation is proposed. This yields the best overall prediction of the SGS viscous dissipation within the inertial subrange. An SGS scalar dissipation model based on the proportionality of the turbulent time scale with the scalar mixing time scale also performs the best for the filter widths in the inertial subrange. Two dynamic methods are implemented for the determination of the model coefficients. The one based on the global equilibrium of dissipation and production is shown to be more satisfactory than the conventional dynamic model.     

Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows

The localized artificial diffusivity method is investigated in the context of large-eddy simulation of compressible turbulent flows. The performance of different artificial bulk viscosity models are evaluated through detailed results from the evolution of decaying compressible isotropic turbulence with eddy shocklets and supersonic turbulent boundary layer. Effects of subgrid-scale (SGS) models and implicit time-integration scheme/time-step size are also investigated within the framework of the numerical scheme used. The use of a shock sensor along with artificial bulk viscosity significantly improves the scheme for simulating turbulent flows involving shocks while retaining the shock-capturing capability. The proposed combination of Ducros-type sensor with a negative dilatation sensor removes unnecessary bulk viscosity within expansion and weakly compressible turbulence regions without shocks and allows it to localize near the shocks. It also eliminates the need for a wall-damping function for the bulk viscosity while simulating wall-bounded turbulent flows. For the numerical schemes used, better results are obtained without adding an explicit SGS model than with SGS model at moderate Reynolds number. Inclusion of a SGS model in addition to the low-pass filtering and artificial bulk viscosity results in additional damping of the resolved turbulence. However, investigations at higher Reynolds numbers suggest the need for an explicit SGS model. The flow statistics obtained using the second-order implicit time-integration scheme with three sub-iterations closely agrees with the explicit scheme if the maximum Courant–Friedrichs–Lewy is kept near unity.